Novel VNS Algorithms on Asymmetric Traveling Salesman Problems

The Asymmetric Traveling Salesman Problem (ATSP) is one of the most studied combinatorial optimization problems. It is a generalized traveling salesman problem in which distances between a pair of cities need not equal in the opposite direction. Since ATSP belongs to a class of NP-hard problems and the optimal solution cannot be found within an appropriate computation time, many researchers have thus paid their attentions to develop effective heuristics to find out good solutions within a short computation time. This paper proposes various VNS algorithms for ATSP in order to find out for the best algorithm among them. Each of these VNS algorithms is developed based on a distinct combination of neighborhood. In order to compare the performances of the VNS algorithms proposed in this research, these VNS algorithms are run on the benchmark ATSP instances, and the results taken from these algorithms are then compared in terms of solution quality.